“Optimization” is a process of finding an “ideal” and/or “best” solution to a given computer problem, as defined by a mathematical function describing a specific problem. Many problems exist which can be described by a mathematical function, wherein the “ideal” or “best” solution to the problem is the global minimum of the mathematical function.
The art of finding the global minimum of a function is referred to as global optimization. Model-based global optimization techniques have been applied to determine the minimum value for complex functions. A well-known example of a model-based global optimization technique is simulated annealing, which is a physical interpretation of a global optimization problem. Simulated annealing utilizes the classical laws of physics to determine a solution. Briefly, the simulated annealing process derives from the roughly analogous physical process of slowly cooling a particle within a system until the particle reaches its ground state. In simulation, a minimum of the function corresponds to this ground state of the particle.
More specifically, as the temperature of the system is lowered, the particle will slide in and out of certain minima. If the temperature is lowered slowly enough, the particle will eventually slide into the global minimum and thus reach its ground state.
Simulated annealing, as well as other known global optimization techniques, decreases in efficiency as the dimensionality (and thus complexity) of a problem grows. For example, when using the simulated annealing method to factor an integer, the computational time to factor the integer can grow (e.g., exponentially) with the size of the integer.